Aptitude Discussion

Q. |
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. What part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup? |

✖ A. |
7/11 |

✖ B. |
6/7 |

✔ C. |
1/5 |

✖ D. |
2/7 |

**Solution:**

Option(**C**) is correct

Suppose the vessel initially contains 8 litres of liquid.

Let $ x $ litres of this liquid be replaced with water then quantity of water in new mixture

$=3-\dfrac{3x}{8}+x$ litres

Quantity of syrup in new mixture $ =5-\dfrac{5x}{8} $ litres

After replacement, the quantity of water and syrup is same in the new mixture.

Therefore,

\begin{align*}

3-\dfrac{3x}{8}+x &= 5-\dfrac{5x}{8}\\

\Rightarrow 5x+24 &=40-5x\\

\Rightarrow 10x &=16\\

\Rightarrow x &=\dfrac{8}{5}

\end{align*}

So part of the mixture replaced,

$ =\dfrac{8}{5}\times \dfrac{1}{8} = \dfrac{1}{5}$

**Chakarya**

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**Kritarth**

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why the answer 8/5 has been multiplied with 1/8 ? please explain...thank u

8 by 5 litre mixure out of 8 litre initial solution is replaced that is 1 by 5 part of initial mixture

**Div**

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please explain it again

**Parul**

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plzz explain it...

**Sim**

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not getting it........

Syrup part is only getting added with water mixture. So,

3/8 + 5x/8 = 1/2

(Water in mix + Syrup getting added with water) = Half of water or syrup

Solving for x, we get x = 1/5